Question

When a wheel with metal spokes,1m long is rotated in a magnetic field of flux density $5\times {{10}^{4}}wb/{{m}^{2}}$ normal to the plane of the wheel , an emf of $0.01v$ is induced between the rim and the axis, the frequency of radius of the wheel is
A) $10\pi$ revolution per second
B)$\dfrac{20}{\pi }$ revolution per second
C)$\dfrac{10}{\pi }$ revolution per second
D)$20\pi$ revolution per second

Answer 1

Spoke is one of some number of rods radiating from the center of a wheel. Spoke are connecting rods between bicycle hub and rim the purpose of the spoke is to transfer the load between the hub and rim, spokes are made of steel and the steel may be a stainless steel or high carbon steel.Faraday’s first laws of electromagnetic induction states that when a conductor is rotating in a magnetic field an emf is induced in a circuit.

Complete step-by-step answer:
Faraday's law of induction which predicts how a magnetic field interacts with an electric field to induce an electromotive force; this phenomenon is known as electrometric induction. Electromagnetic induction principle is used in transformers generators and many other devices.
Faraday's second of electromagnetic induction states that the rate of change of flux linkages is equal to the induced EMF
$e=-N\dfrac{dQ}{dt}volts$
Negative sign represents the direction of the induced current will be in opposite direction
From the data $B=5\times {{10}^{-4}}$ , $l=0.5m$
$v=l\omega$
A wheel with metal spokes,1m long is rotated
So $v=1\times \omega =\omega$
An EMF of $0.01v$ is induced between the rim and axis is given by:
$EMF=Blv$
After substituting the values in the above equation
$\begin{aligned} & 0.01=5\times {{10}^{-4}}\times 0.5\times \omega \\\ & 1=5\times {{10}^{-2}}\times 0.5\times \omega \\\ & 1=2.5\times {{10}^{-2}}\omega \\\ & \omega =\dfrac{1\times {{10}^{-2}}}{2.5} \\\ & \omega =40rad/\sec \\\ \end{aligned}$
We know that $1rps=2\pi rad/\sec$
$\omega =\dfrac{40rad/\sec }{2\pi }=\dfrac{20}{\pi }rps$

So, the correct answer is “Option B”.

Note: Student the emf induced between the center and the rim can be obtained by Faraday's laws and also by motional emf. Emf induced is independent upon the number of spokes, number of spokes may be 3 or else 6 and it depends upon the velocity. The lighter wheel performs better than the stronger wheel.